[FOM] Predicativism and natural numbers

[Giovanni Lagnese]

Nik Weaver wrote:

> I start with the idea that words like "set" and "collection"
> have no literal referents.  Actually, it surprises me that
> this is not taken for granted by modern philosophers.
> Ordinary language assertions involving such words
> can always be rephrased in equivalent ways which
> do not use such words.

I think that no word has "literal referents", because in the natural world 
there are no objects.
Objects are our categories that we use to modeling the natural world.
Similarly, sets are our categories that we use to modeling the natural 
world.
I think that this does not exclude a conceptualistic view about foundation 
of mathematics.
In my opinion, the point is not giving sense to words, but giving sense to 
statements.
The point is not identifying a structure which plays the role of the set of 
natural numbers, but giving sense to quantification in the set of natural 
numbers.
Similarly, the point is not identifying a structure which plays the role of 
the powerset of natural numbers, but giving sense to quantification in the 
powerset of natural numbers.
I think we can give sense to quantification in the powerset of natural 
numbers by assuming something like Brouwer's continuity principle.

GL